# Photon energy

The photon energy is the energy carried by a single photon with a certain electromagnetic wavelength and frequency. The higher the photon's frequency, the higher its energy. Equally, the longer the photon's wavelength, the lower its energy.

Photon energy is solely a function of the photon's wavelength. Other factors, such as the intensity of the radiation, do not affect photon energy. In other words, two photons of light with the same color (and, therefore, same frequency) will have the same photon energy, even if one was emitted from a wax candle and the other from the Sun.

The photon energy can be represented by any unit of energy. Among the units commonly used to denote photon energy are the electronvolt (eV) and the joule (as well as its multiples, such as the microjoule). As one joule equals 6.24 × 1018 eV, the larger units may be more useful in denoting the energy of photons with higher frequency and higher energy, such as gamma rays, as opposed to lower energy photons, such as those in the radiofrequency region of the electromagnetic spectrum.

Photons being massless, the notion of "photon energy" is not related to mass through the equivalence E = mc2.

## Formula

The equation for photon energy[1] is

$E = \frac{hc}{\lambda}$

Where E is the photon energy, h is the Planck constant, c is the speed of light in vacuum and λ is the photon's wavelength. As h and c are both constants, the photon energy changes with direct relation to wavelength λ.

To find the photon energy in electronvolts, using the wavelength in micrometres, the equation is approximately

$E(eV) = \frac{1.2398}{\mathrm{\lambda}({\mu}m)}$

Therefore, the photon energy at 1 μm wavelength (the wavelength of near infrared radiation) is approximately 1.2398 eV.

Since $\frac{c}{\lambda} = f$, where f is frequency, the photon energy equation can be simplified to

$E = hf$

This equation is known as the Planck-Einstein relation. Substituting h with its value in J⋅s and f with its value in hertz gives the photon energy in joules. Therefore, the photon energy at 1 Hz frequency is 6.62606957 × 10-34 joules or 4.135667516 × 10-15 eV.

## Examples

An FM radio station transmitting at 100 MHz emits photons with an energy of about 4.1357 × 10-7 eV. This minuscule amount of energy is approximately 8 × 10-13 times the electron's mass (via the mass-energy equivalence).

The highest energy gamma rays detected to date, very-high-energy gamma rays, have a photon energy of 100 GeV to 100 TeV (1011 to 1014 electronvolts) or 0.01602 microjoules to 0.01602 millijoules. This corresponds to frequencies of 2.42 × 1025 to 2.42 × 1028 Hz.

A photon with a wavelength equal to the Planck length would have an energy of about 7.671 × 1028 eV or 1.229 × 1010 joules (12.29 gigajoules). This is roughly the amount of energy produced by the world's most powerful coal-fired power station, the Taichung Power Plant, during a period of 2.25 seconds.